Putting Bills Into a Machine

This is a continuation of last week’s discussion. You might want to check that blog out for context.

Consider the values of these combinations, playing 9/6 Jacks or Better for dollars, five coins at a time. Note that the value of these combinations can vary depending on the other two cards in the hands. In the examples so far, I’m considering the fourth and fifth card to be an unsuited 2 and 3.

SF3+1 SF3 2h1i QJ9 $3.70
SF3 1h0i JT9 $3.68
SF3+0 SF3 2h2i QJ8 $3.21
SF3 1h1i JT8 $3.20
SF3 0h0i 987 $3.18
SF3-1 SF3 1h2i QT8 $2.72
SF3 0h1i 986 $2.70
SF3-2 SF3 0h2i 874 $2.22

Within each of the four SF3 categories (SF3+1; SF3+0; SF3-1; SF3-2), you’ll see that each example is worth very close to the same amount, and that the difference in value between the categories is approximately 50 cents each time. In this particular game, adding (or subtracting) a high card is equal to almost exactly the same amount as subtracting (or adding) a gap, or inside.

With this information, it’s not hard to conclude that however you play, say, QJ8 in a hand, you’ll play 987 the same way. Figuring out which of these two examples of an SF3+0 is being discussed in a particular hand shouldn’t be confusing because in games without wild cards, it’s impossible to have two separate SF3 combinations in the same five cards.

And it shouldn’t be surprising that there might be hands where you’d play QJ8 differently than you’d play QT8, simply because QJ8 is worth about 50 cents more. 

Coming to these conclusions takes you a long way from treating all 3-card straight flush combinations the same. And having four SF3 categories (in the first column) is a lot easier to deal with than listing eight separate types of hands (in the second column). 

In addition to removing four lines of strategy from the basic strategy chart, using this notation provides part of a shorthand to discuss more complicated hands. While a complete discussion of straight penalties, flush penalties, and various other types of penalties is beyond what I want to talk about today, understanding the categorization of SF3s is the first step to being able to understand our advanced strategies.

Now consider 10-7 (or 9-7) Double Bonus. When we’re dealing with SF3s, the amount you receive for the full house is irrelevant because full houses only have two different ranks of cards in them and SF3s have three. While two pair as a final hand is definitely possible when starting from an SF3, the probability of ending up with two pair affects all these hands identically — so it doesn’t matter in ranking these hands whether we get paid five coins or ten for two pair. Compared to Jacks or Better, Double Bonus pays more for the flush and more for the straight. See how the values of our SF3s change in this game:

SF3+1 SF3 2h1i QJ9 $3.91
SF3 1h0i JT9 $3.95
SF3+0 SF3 2h2i QJ8 $3.36
SF3 1h1i JT8 $3.41
SF3 0h0i 987 $3.46
SF3-1 SF3 1h2i QT8 $2.86
SF3 0h1i 986 $2.91
SF3-2 SF3 0h2i 874 $2.36

In Double Bonus, all of the SF3s are worth more than they were in Jacks or Better and the SF3s in each category aren’t clustered so tightly. In these examples, you’ll see that when you reduce the number of high cards by one unit and increase the number of insides, the value of the SF3 goes up by about a nickel. 

Our SF3 simplification still works, but not quite so perfectly.

Another example is Triple Bonus Poker Plus. In this game, flushes get paid only 5-for-1 (instead of 6-for-1 in Jacks or Better and 7-for-1 in Double Bonus) but straight flushes get paid 100-for-1 instead of 50-for-1 in the other two games. Let’s see how that affects the value of our combinations.

SF3+1 SF3 2h1i QJ9 $3.83
SF3 1h0i JT9 $4.05
SF3+0 SF3 2h2i QJ8 $3.12
SF3 1h1i JT8 $3.33
SF3 0h0i 987 $3.55
SF3-1 SF3 1h2i QT8 $2.62
SF3 0h1i 986 $2.84
SF3-2 SF3 0h2i 874 $2.12

Here the combinations are not nearly so clustered as they were in the other two games. Getting paid twice as much for a straight flush adds a lot more to the value of an SF3 without insides than it does to an SF3 with one or more insides. Remember, an SF3 with two insides has the potential to become one straight flush only. An SF3 with one inside has the potential to turn into two straight flushes, and an SF3 with no inside has the potential to turn into three different straight flushes.

Because of this, in one case on the strategy for this game, we have to separate the two types of SF3-1. On a hand like “KQ” 346, hold 346. (346 has the same value as 875 in the previous chart. Both have no high cards and one inside.) On a hand like “KQ” A35, we hold “KQ”. A35 (one high card and two insides) is worth the same as QT8 and as our chart above says, A35 is worth 22 cents less than 346

In my personal Triple Bonus Poker Plus strategy, however, I still use the SF3 notation discussed in the last two weeks. But when it doesn’t fit (as in the hands discussed in the previous paragraph), I resort to the clumsier notation. There is value to use the same notation in all strategies — but I don’t force it when it isn’t a good fit.


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